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revised some tensor contraction
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@chakravala
chakravala committed Jun 24, 2024
1 parent 1416e12 commit 2493c4d
Showing 1 changed file with 53 additions and 5 deletions.
58 changes: 53 additions & 5 deletions src/forms.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -290,6 +290,8 @@ end

export TensorNested
abstract type TensorNested{V,T} <: Manifold{V,T} end
@pure Manifold(::T) where T<:TensorNested{V} where V = V
@pure Manifold(::Type{T}) where T<:TensorNested{V} where V = V

transpose_row(t::Values{N,<:Chain{V}},i,W=V) where {N,V} = Chain{W,1}(getindex.(t,i))
transpose_row(t::FixedVector{N,<:Chain{V}},i,W=V) where {N,V} = Chain{W,1}(getindex.(t,i))
Expand Down Expand Up @@ -409,6 +411,8 @@ struct DiagonalOperator{V,T<:TensorAlgebra{V}} <: TensorNested{V,T}
DiagonalOperator(t::T) where {V,T<:TensorAlgebra{V}} = new{V,T}(t)
end

(T::DiagonalOperator{V})(x::TensorAlgebra{V}) where V = contraction(T,x)

value(t::DiagonalOperator) = t.v
matrix(m::DiagonalOperator) = matrix(TensorOperator(m))
getindex(t::DiagonalOperator,i::Int,j::Int) = i≠j ? zero(valuetype(value(t))) : value(t)[i]
Expand Down Expand Up @@ -452,6 +456,7 @@ struct TensorOperator{V,W,T<:TensorAlgebra{V,<:TensorAlgebra{W}}} <: TensorNeste
end

Endomorphism{V,T<:TensorAlgebra{V,<:TensorAlgebra{V}}} = TensorOperator{V,V,T}
(T::TensorOperator{V})(x::TensorAlgebra{V}) where V = contraction(T,x)

value(t::TensorOperator) = t.v
matrix(m::TensorOperator) = matrix(value(m))
Expand Down Expand Up @@ -534,6 +539,7 @@ end
:(Outermorphism{V}($(Expr(:tuple,[:(compound(t,Val($g))) for g ∈ list(1,mdims(V))]...))))
end

(T::Outermorphism{V})(x::TensorAlgebra{V}) where V = contraction(T,x)
Outermorphism(t::Simplex) = outermorphism(t)
Outermorphism(t::Endomorphism{V,<:Simplex}) where V = outermorphism(value(t))
outermorphism(t::Endomorphism{V,<:Simplex}) where V = outermorphism(value(t))
Expand Down Expand Up @@ -597,6 +603,13 @@ outer(a::Leibniz.Derivation,b::Chain{V,1}) where V= outer(V(a),b)
outer(a::Chain{W},b::Leibniz.Derivation{T,1}) where {W,T} = outer(a,W(b))
outer(a::Chain{W},b::Chain{V,1}) where {W,V} = Chain{V,1}(a.*value(b))

contraction_metric(a::TensorNested,b::TensorNested,g) = contraction(a,b)
contraction_metric(a::TensorNested,b::TensorAlgebra,g) = contraction(a,b)
contraction_metric(a::TensorAlgebra,b::TensorNested,g) = contraction(a,b)
wedgedot_metric(a::TensorNested,b::TensorNested,g) = a⟑b
wedgedot_metric(a::TensorNested,b::TensorAlgebra,g) = a⟑b
wedgedot_metric(a::TensorAlgebra,b::TensorNested,g) = a⟑b

contraction(a::Proj,b::TensorGraded) = a.v⊗(a.λ*(a.v⋅b))
contraction(a::Dyadic,b::TensorGraded) = a.x⊗(a.y⋅b)
contraction(a::TensorGraded,b::Dyadic) = (a⋅b.x)⊗b.y
Expand Down Expand Up @@ -624,7 +637,7 @@ contraction(a::Submanifold{W},b::Chain{V,G,<:Chain}) where {W,G,V} = Chain{V,G}(
contraction(a::Single{W},b::Chain{V,G,<:Chain}) where {W,G,V} = Chain{V,G}(column(Ref(a).⋅value(b)))
contraction(x::Chain{V,G,<:Chain},y::Single{V,G}) where {V,G} = value(y)*x[bladeindex(mdims(V),UInt(basis(y)))]
contraction(x::Chain{V,G,<:Chain},y::Submanifold{V,G}) where {V,G} = x[bladeindex(mdims(V),UInt(y))]
contraction(a::Chain{V,L,<:Chain{V,G},N},b::Chain{V,G,<:Chain{V},M}) where {V,G,L,N,M} = Chain{V,G}(contraction.(Ref(a),value(b)))
#contraction(a::Chain{V,L,<:Chain{V,G},N},b::Chain{V,G,<:Chain{V},M}) where {V,G,L,N,M} = Chain{V,G}(contraction.(Ref(a),value(b)))
contraction(x::Chain{V,L,<:Chain{V,G},N},y::Chain{V,G,<:Chain{V,L},N}) where {L,N,V,G} = Chain{V,G}(contraction.(Ref(x),value(y)))
contraction(x::Chain{W,L,<:Chain{V,G},N},y::Chain{V,G,T,N}) where {W,L,N,V,G,T} = Chain{V,G}(matmul(value(x),value(y)))
contraction(x::Chain{W,L,<:Multivector{V},N},y::Chain{V,G,T,N}) where {W,L,N,V,G,T} = Multivector{V}(matmul(value(x),value(y)))
Expand All @@ -634,16 +647,22 @@ contraction(x::Multivector{W,<:Multivector{V},N},y::Multivector{V,T,N}) where {W
Expr(:call,:Values,[Expr(:call,:+,:(@inbounds y[$i]*value(x[$i]))) for i ∈ list(1,N)]...)
end
@inline @generated function matmul(x::Values{N,<:Chain{V,G}},y::Values{N}) where {N,V,G}
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds y[$i]*x[$i][$j]) for i ∈ list(1,N)]...) for j ∈ list(1,binomial(mdims(V),G))]...)
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds x[$i][$j]*y[$i]) for i ∈ list(1,N)]...) for j ∈ list(1,binomial(mdims(V),G))]...)
end
@inline @generated function matmul(x::Values{N,<:Multivector{V}},y::Values{N}) where {N,V}
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds y[$i]*value(x[$i])[$j]) for i ∈ list(1,N)]...) for j ∈ list(1,1<<mdims(V))]...)
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds value(x[$i])[$j]*y[$i]) for i ∈ list(1,N)]...) for j ∈ list(1,1<<mdims(V))]...)
end
@inline @generated function matmul(x::Values{N,<:Spinor{V}},y::Values{N}) where {N,V}
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds y[$i]*value(x[$i])[$j]) for i ∈ list(1,N)]...) for j ∈ list(1,1<<(mdims(V)-1))]...)
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds value(x[$i])[$j]*y[$i]) for i ∈ list(1,N)]...) for j ∈ list(1,1<<(mdims(V)-1))]...)
end
@inline @generated function matmul(x::Values{N,<:AntiSpinor{V}},y::Values{N}) where {N,V}
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds y[$i]*value(x[$i])[$j]) for i ∈ list(1,N)]...) for j ∈ list(1,1<<(mdims(V)-1))]...)
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds value(x[$i])[$j]*y[$i]) for i ∈ list(1,N)]...) for j ∈ list(1,1<<(mdims(V)-1))]...)
end
@inline @generated function matwedge(x::Values{N,<:Chain{V,G}},y::Values{N}) where {N,V,G}
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds x[$i][$j]∧y[$i]) for i ∈ list(1,N)]...) for j ∈ list(1,binomial(mdims(V),G))]...)
end
@inline @generated function matvee(x::Values{N,<:Chain{V,G}},y::Values{N}) where {N,V,G}
Expr(:call,:Values,[Expr(:call,:+,[:(@inbounds x[$i][$j]∨y[$i]) for i ∈ list(1,N)]...) for j ∈ list(1,binomial(mdims(V),G))]...)
end

contraction(x::Spinor{W,<:Spinor{V},N},y::Spinor{V,T,N}) where {W,N,V,T} = Spinor{V}(matmul(value(x),value(y)))
Expand Down Expand Up @@ -682,6 +701,21 @@ minus(a::TensorNested,b::TensorNested) = a+(-b)
@inline ⟑(a::Chain{V,G,<:Chain{V,G}} where {V,G},b::TensorNested) = contraction(a,b)
@inline ⟑(a::TensorNested,b::Chain{V,G,<:Chain{V,G}} where {V,G}) = contraction(a,b)

for (op,po) ∈ ((:∧,:.∧),(:∨,:.∨))
@eval begin
$op(a::DiagonalOperator{V,<:Chain{V,G}},b::Chain{V,G}) where {V,G} = Chain{V,G}($po(value(value(a)),value(b)))
$op(a::DiagonalOperator{V,<:Chain{V,G}},b::DiagonalOperator{V,<:Chain{V,G}}) where {V,G} = DiagonalOperator(Chain{V,G}($po(value(value(a)),value(value(b)))))
#$op(a::Endomorphism{W,<:TensorGraded},b::Endomorphism{V,<:Chain{V,G}}) where {W,V,G} = TensorOperator(Chain{V,G}($po(Ref(value(a)),value(value(b)))))
$op(a::Endomorphism{W,<:TensorGraded},b::Endomorphism{V,<:Chain{V,G}}) where {W,V,G} = TensorOperator(Chain{V,G}($po(Ref(a),value(value(b)))))
#$op(x::Chain{W,L,<:Chain{V,G},N},y::Chain{V,G,<:Chain{X,F} where {X,F},N}) where {W,L,N,V,G} = Chain{V,G}($po(Ref(x),value(y)))
end
end
∧(a::Endomorphism{W,<:Chain},b::Chain{V,G}) where {W,V,G} = Chain{V,G}(matwedge(value(value(a)),value(b)))
∨(a::Endomorphism{W,<:Chain},b::Chain{V,G}) where {W,V,G} = Chain{V,G}(matvee(value(value(a)),value(b)))
for op ∈ (:complementright,:complementleft,:complementrighthodge,:complementlefthodge,:metric,:cometric)
@eval $op(a::Endomorphism{V,<:Chain}) where V = map($op,a)
end

contraction(a::DiagonalOperator{V,<:Chain{V,G}},b::Chain{V,G}) where {V,G} = Chain{V,G}(value(value(a)).*value(b))
contraction(a::Chain{V,G},b::DiagonalOperator{V,<:Chain{V,G}}) where {V,G} = Chain{V,G}(value(a).*value(value(b)))
contraction(a::DiagonalOperator{V,<:Chain{V,G}},b::DiagonalOperator{V,<:Chain{V,G}}) where {V,G} = DiagonalOperator(Chain{V,G}(value(value(a)).*value(value(b))))
Expand Down Expand Up @@ -710,6 +744,14 @@ end
Expr(:call,:(Multivector{V}),Expr(:call,:Values,:(@inbounds value(b)[1]),[:(value(contraction((@inbounds a.v[$g]),b(Val($g))))...) for g ∈ list(1,mdims(V))]...))
end

scalarcheck(x) = isscalar(x) ? value(scalar(x)) : x
for (op,args) ∈ ((:contraction,()),(:contraction_metric,(:g,)))
@eval @generated function $op(x::Endomorphism{V,<:Chain{V,G,<:Chain{V,G,<:TensorGraded{W,L}}}},y::TensorGraded{W,L},$(args...)) where {W,L,V,G}
Expr(:call,:TensorOperator,Expr(:call,:(Chain{V,G}),[Expr(:call,:(Chain{V,G}),
[:(@inbounds scalarcheck($$op(x[$i][$j],y,$($args...)))) for i ∈ list(1,gdims(mdims(V),G))]...) for j ∈ list(1,gdims(mdims(V),G))]...))
end
end

for op ∈ (:plus,:minus,:+,:-)
@eval @generated function $op(a::Outermorphism{V},b::Outermorphism{V}) where V
Expr(:call,:(Outermorphism{V}),Expr(:tuple,[:($$op(value(a)[$g],value(b)[$g])) for g ∈ list(1,mdims(V))]...))
Expand Down Expand Up @@ -749,6 +791,12 @@ for F ∈ Fields
end
end

Base.map(fn, x::DiagonalOperator) = DiagonalOperator(map(fn,value(x)))
Base.map(fn, x::TensorOperator{V,W,<:Chain{V,G}}) where {V,W,G} = TensorOperator(Chain{V,G}(map.(fn,value(value(x)))))
Base.map(fn, x::TensorOperator{V,W,<:Spinor}) where {V,W} = TensorOperator(Spinor{V}(map.(fn,value(value(x)))))
Base.map(fn, x::TensorOperator{V,W,<:AntiSpinor}) where {V,W} = TensorOperator(AntiSpinor{V}(map.(fn,value(value(x)))))
Base.map(fn, x::TensorOperator{V,W,<:Multivector}) where {V,W} = TensorOperator(Multivector{V}(map.(fn,value(value(x)))))

# dyadic identity element

for op ∈ (:(Base.:+),:(Base.:-))
Expand Down

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Registration pull request created: JuliaRegistries/General/109694

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